The 48-year-old will bring the experience of being a former head coach of Sri Lanka and Bangladesh to the job.
"I am excited at the opportunity to contribute to what I think is an interesting time for West Indies. I think this assignment has come at an important time of my career," said Law.
Law played just one Test for Australia in his career but featured in 54 one-day internationals while building a solid first-class career with Queensland, Essex, Lancashire and Derbyshire.
Outgoing director of cricket at the West Indies Cricket Board (WICB), Richard Pybus said: "We are delighted to welcome Stuart, he comes at an exciting and critical time in the development of the West Indies men's team.
"He has great experience and breadth of knowledge as a player and coach and his cross-cultural experience and winning attitude will be key assets in the development of the team.
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